Question

Taco Corp. is planning to construct a hyperloop between Chicago and Springfield, Illinois. A hyperloop is a tube through which people or goods can be transported at very rapid speeds. The hyperloop would rely upon three inputs: capital, labor, and fuel. A production function for the hyperloop has been estimated as: T = aKbLcFd = 0.02K0.25L0.2 F0.55 where T = the number of trips taken through the loop annually, K is capital, L is labor, and F is fuel.

a. If Taco employs 100 units of capital, 500 units of labor and 20,000 units of fuel, calculate the marginal products if Taco increases input use by 1 for K, L and F.

b. What is Taco's marginal rate of technical substitution (MRTS) between K and L? What about MRTS between K and F? Would Taco try to ensure that all its MRTSs are equal? Why?

c. Does the law of diminishing returns apply to K in the production of trips between Chicago and Springfield? What about to L or F? Why do you say this? Would the law of diminishing returns apply to L if c = -0.2 instead of 0.2? What if c = 1.2?

d. Taco's production function exhibit constant, increasing or decreasing returns to scale? Why do you say this? Would your answer change if c = -0.2 instead of 0.2? What if c = 1.2?

Answer 1